Method and system for detecting deposits in a vessel

ABSTRACT

Systems and methods for detecting a deposit in a vessel with a sensing cable including an optical fiber sensor array aligned with a heating element disposed in the vessel. An excitation source is configured to propagate at least one heat pulse through the heating element along at least a portion of the sensing cable to affect an exchange of thermal energy between the heating element and media exposed to the sensing cable. An optical signal interrogator is adapted to receive a signal from a plurality of sensor locations and configured to measure, a temperature profile corresponding to the heat pulse at the sensor locations. A control unit is configured to detect a deposit by determining one or more properties of the one or more media exposed to the sensing cable at each of the plurality of sensor locations based on the temperature profile corresponding thereto.

CROSS REFERENCE TO RELATED APPLICATION

This application relates and claims priority to U.S. Provisional PatentApplication No. 61/806,107, filed on Mar. 28, 2013.

FIELD

The presently disclosed subject matter relates to methods and systemsfor detecting deposits in a vessel. More particularly, the presentlydisclosed subject matter relates to detecting deposits in a vessel usinga sensing cable including an optical fiber sensor array aligned with aheating element.

BACKGROUND

Components of certain equipment, such as that used in the petroleum andpetrochemical industry, which includes the exploration, production,refining, manufacture, supply, transport, formulation or blending ofpetroleum, petrochemicals, or the direct compounds thereof, are oftenmonitored to maintain reliable operation. However, such components caninvolve harsh conditions, such as high temperature, high pressure,and/or a corrosive environment, making it difficult or costly to obtainreliable measurements.

Deposits, such as debris, bio-growth, inorganic or organic fouling,coking, or the like, on the surface of a component in connection withpetroleum and petrochemical operations, such as those in refineries,chemical plants, and oil and gas processing plants, are generallyundesirable. For example, deposits on components such wash beds, trays,or packing of distillation towers, reactors, heat exchangers, furnacetubes, or the like can cause unplanned capacity loss, excessive cost ofequipment maintenance, and increased energy usage.

Undesirable deposits can result from a number of causes in a refinery orthe like. For example, the processing of a hydrocarbon-containing feedstreams at elevated temperatures in a processing zone, such as afurnace, heat exchanger, distillation tower or other refinery equipment,can result in the formation of carbonaceous substances which can depositon surfaces of the equipment. Such carbonaceous substances are generallyreferred to as “coke” in the fields of petroleum refining andpetro-chemical processes. Coke deposition on equipment surfaces canalter the operation of the equipment, usually in an undesirable manner.For example, feed streams are heated in a furnace before beingintroduced to distillation columns. Formation of coke can result in ablockage of tubes in the furnace, as well as the blockage in thetransfer lines from the furnace to the distillation column. The cokingon tube surfaces can also decrease the heat transfer, and thereforereduce the energy efficiency of the furnace. Additionally, coking oftenoccurs in the column itself, typically within wash beds or at interfacesbetween different types of packing or the like. Coking can also occur inthe bottom of the tower and plug liquid outlets and pump strainers,causing pump cavitation and damage.

Measurement of the distribution of deposits, such as coke, can providefor enhanced operation strategies. For example, detection of the onsetof coking in a wash bed of a vacuum pipe still distillation tower canallow mitigation techniques (such as application of a high flow rate ofwash oil) to be appropriately applied.

Conventional techniques for detection of such deposits can include pointmeasurements (e.g., using ultrasonic thickness measurements), pressuredrop measurements, and bulk heat transfer estimation techniques. Forexample, detection of coking in refinery equipment, includingdistillation towers, distillation tower bottom circuits, distillationtower feed furnaces, and coker feed furnaces and transfer lines, hasbeen addressed with measurement of pressure drop. However, thistechnique is not without disadvantages, such as for vacuum tower washbeds, where the pressure drop is typically only on the order of a fewmmHg in these wash beds when coking occurs. Additionally, pressuremeasurements cannot tell where (either the axial location or thediametric location) the deposits are occurring in the wash bed. Thus,pressure measurement can be a highly unreliable indicator of coking.Similarly, temperature differentials between bulk temperatures have alsobeen used to detect coking. However, this technique involves a grossmeasurement and thus not necessarily accurate.

Accordingly, there is a continued need for improved techniques fordetecting deposits in a vessel.

SUMMARY

The purpose and advantages of the disclosed subject matter will be setforth in and apparent from the description that follows, as well as willbe learned by practice of the disclosed subject matter. Additionaladvantages of the disclosed subject matter will be realized and attainedby the methods and systems particularly pointed out in the writtendescription and claims hereof, as well as from the appended drawings. Toachieve these and other advantages and in accordance with the purpose ofthe disclosed subject matter, as embodied and broadly described, thedisclosed subject matter includes systems and methods for detecting adeposit in a vessel.

In accordance with one aspect of the disclosed subject matter, a methodfor detecting a deposit in a vessel includes providing within a vessel asensing cable including an optical fiber sensor array aligned with aheating element. The method includes propagating at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable. Themethod includes measuring, over time, a temperature profile of thesensing cable corresponding to the heat pulse at each of a plurality ofsensor locations on the optical fiber sensor array. The method includesdetecting a deposit by determining one or more properties of the one ormore media exposed to the sensing cable at each of the plurality ofsensor locations based on the temperature profile corresponding thereto.

In certain embodiments, the vessel can include a vacuum pipe stilldistillation tower, a reactor, a heat exchanger, or a furnace tube.Detecting the deposit can include detecting debris, bio-growth,inorganic fouling, organic fouling, or coking. As embodied herein,measuring the temperature profile corresponding to the heat pulse ateach of the plurality of sensor locations can include, for each sensorlocation, measuring a plurality of temperatures over a period of timeupon arrival of the heat pulse at the sensor location. Detecting thedeposit can include, for each temperature profile, performing aregression of the plurality of temperatures over a logarithm ofcorresponding measurement times for a predetermined time window in theperiod of time to generate a slope and an intercept of the regression,wherein the slope and the intercept relate to the one or more propertiesof the material exposed to the sensing cable at the sensor location.Additionally or alternatively, detecting the deposit can include, foreach temperature profile, generating a time derivative by calculating aderivative of the plurality of temperature measurements with respect totime, applying a transform to the time derivative to generate a complexspectrum, and determining an amplitude and a phase of the complexspectrum, wherein the amplitude and the phase of the complex spectrumrelate to the one or more properties of the material exposed to thesensing cable at the sensor location. Detecting the deposit can furtherinclude generating a frequency derivative spectrum by calculating thederivative of the complex spectrum with respect to frequency, anddetermining an amplitude and a phase of the frequency derivativespectrum, wherein the amplitude and the phase of the frequencyderivative spectrum relate to the one or more properties of the materialexposed to the sensing cable at the sensor location.

In accordance with another aspect of the disclosed subject matter, asystem for detecting a deposit in a vessel includes a sensing cableincluding an optical fiber sensor array aligned with a heating elementdisposed in the vessel, the optical fiber sensor array having aplurality of sensor locations. The system includes an excitation sourcecoupled with the heating element and configured to propagate at leastone heat pulse through the heating element along at least a portion ofthe sensing cable to affect an exchange of thermal energy between theheating element and the one or more media exposed to the sensing cable.The system includes an optical signal interrogator coupled with theoptical fiber sensor array and adapted to receive a signal from each ofthe plurality of sensor locations and configured to measure, over time,a temperature profile of the sensing cable corresponding to the heatpulse at each of the plurality of sensor locations on the optical fibersensor array. The system includes a control unit, coupled with theheating element and the optical signal interrogator, to detect a depositby determining one or more properties of the one or more media exposedto the sensing cable at each of the plurality of sensor locations basedon the temperature profile corresponding thereto.

In certain embodiments, the vessel can include a vacuum pipe stilldistillation tower, a reactor, a heat exchanger, or a furnace tube. Thedeposit can include debris, bio-growth, inorganic fouling, organicfouling, or coking. As embodied herein, the optical signal interrogatorcan be configured, for each of the plurality of sensor locations, tomeasure a plurality of temperatures over a period of time upon arrivalof the heat pulse at the sensor location. the control unit can beconfigured, for each temperature profile, to perform a regression of theplurality of temperatures over a logarithm of corresponding measurementtimes for a predetermined time window in the period of time to generatea slope and an intercept of the regression, wherein the slope and theintercept relate to the one or more properties of the material exposedto the sensing cable at the sensor location. Additionally oralternatively, the control unit can be configured, for each temperatureprofile, to generate a time derivative by calculating a derivative ofthe plurality of temperature measurements with respect to time, apply atransform to the time derivative to generate a complex spectrum, anddetermine an amplitude and a phase of the frequency derivative spectrum,wherein the amplitude and the phase of the frequency derivative spectrumrelate to the one or more properties of the material exposed to thesensing cable at the sensor location. The control unit can further beconfigured to generate a frequency derivative spectrum by calculatingthe derivative of the complex spectrum with respect to frequency, anddetermine an amplitude and a phase of the frequency derivative spectrum,wherein the amplitude and the phase of the frequency derivative spectrumrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and are intended toprovide further explanation of the disclosed subject matter claimed.

The accompanying drawings, which are incorporated in and constitute partof this specification, are included to illustrate and provide a furtherunderstanding of the disclosed subject matter. Together with thedescription, the drawings serve to explain the principles of thedisclosed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1A is a schematic diagram of an exemplary sensing system inaccordance with the disclosed subject matter.

FIG. 1B is a cross sectional view of an exemplary sensing cableconfiguration in accordance with the disclosed subject matter.

FIG. 1C is a cross sectional view of another exemplary sensing cableconfiguration in accordance with the disclosed subject matter.

FIG. 2 depicts a representative plot of current and heat pulses andcorresponding temperature response in accordance with the disclosedsubject matter.

FIG. 3 is a graph illustrating a direct temperature sensing techniquefor a plurality of sensor locations in accordance with the disclosedsubject matter.

FIG. 4A is a graph illustrating log-time regression sensing technique inaccordance with the disclosed subject matter.

FIG. 4B is a graph illustrating log-time regression sensing techniquefor a plurality of sensor locations in accordance with the disclosedsubject matter.

FIG. 5A is a graph illustrating thermal excitation energy concentrationat harmonics and fundamental frequencies of heat pulses in connectionwith a frequency spectrum sensing technique.

FIG. 5B is a graph illustrating the phase of a frequency-derivativespectrum in connection with frequency spectrum sensing techniques over aplurality of sensor locations in accordance with the disclosed subjectmatter.

FIG. 5C is a graph illustrating the amplitude of a frequency-derivativespectrum in connection with frequency spectrum sensing techniques over aplurality of sensor locations in accordance with the disclosed subjectmatter.

FIG. 6 is a schematic cross sectional view of a representativeembodiment of a shield for a cable configuration in accordance with anexemplary embodiment of the disclosed subject matter.

FIG. 7 is a schematic representation of a system for detecting a depositin a vessel in accordance with an exemplary embodiment of the disclosedsubject matter.

FIG. 8 is a schematic representation of a plurality of sensing cablesarranged in grid patterns in accordance with an exemplary embodiment ofthe disclosed subject matter.

FIG. 9A is an image and graph illustrating an exemplary system andmethod for detecting a deposit in a vessel in accordance with thedisclosed subject matter.

FIG. 9B is an image and graph illustrating another example of a systemand method for detecting a deposit in a vessel in accordance with thedisclosed subject matter.

FIG. 9C is an image and graph illustrating another example of a systemand method for detecting a deposit in a vessel in accordance with thedisclosed subject matter.

FIG. 9D is an image and graph illustrating another example of a systemand method for detecting a deposit in a vessel in accordance with thedisclosed subject matter.

DETAILED DESCRIPTION

As noted above and in accordance with one aspect of the disclosedsubject matter, methods disclosed herein include detecting a deposit ina vessel with a sensing cable including an optical fiber sensor arrayaligned with a heating/cooling element. The method includes propagatingat least one heating/cooling pulse through the heating/cooling elementalong at least a portion of the sensing cable to affect an exchange ofthermal energy between the heating element and one or more media exposedto the sensing cable. The method includes measuring, over time, atemperature profile of the sensing cable corresponding to the heat pulseat each of a plurality of sensor locations on an optical fiber sensorarray. The method includes detecting a deposit by determining one ormore properties of the materials exposed to the sensing cable at each ofthe plurality of sensor locations based on the temperature profilecorresponding thereto.

Furthermore, systems for detecting a deposit in a vessel are alsoprovided. Such systems include a sensing cable including an opticalfiber sensor array aligned with a heating element disposed in thevessel, the optical fiber sensor array having a plurality of sensorlocations. The system further includes an excitation source coupled withthe heating element and configured to propagate at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable. Thesystem also includes an optical signal interrogator coupled with theoptical fiber sensor array and adapted to receive a signal from each ofthe plurality of sensor locations and configured to measure, over time,a temperature profile of the sensing cable corresponding to the heatpulse at each of the plurality of sensor locations on the optical fibersensor array. A control unit, coupled with the heating element and theoptical signal interrogator, detects a deposit by determining one ormore properties of the one or more media exposed to the sensing cable ateach of the plurality of sensor locations based on the temperatureprofile corresponding thereto.

Reference will now be made in detail to the various exemplaryembodiments of the disclosed subject matter, exemplary embodiments ofwhich are illustrated in the accompanying drawings. The accompanyingfigures, where like reference numerals refer to identical orfunctionally similar elements, serve to further illustrate variousembodiments and to explain various principles and advantages all inaccordance with the disclosed subject matter. The accompanying figures,where like reference numerals refer to identical or functionally similarelements, serve to further illustrate various embodiments and to explainvarious principles and advantages all in accordance with the disclosedsubject matter. For purpose of explanation and illustration, and notlimitation, exemplary embodiments of the disclosed subject matter areshown in FIGS. 1-9.

In accordance with the disclosed subject matter, characteristics of oneor more materials can be measured with the use of an optical fibersensor array having a plurality of sensor locations aligned with aheating/cooling element in a sensing cable. At least one heating/coolingpulse is propagated through the heating/cooling element along at least aportion of the sensing cable to affect an exchange of thermal energybetween the heating/cooling element and one or more media exposed to thesensing cable. A temperature profile of the sensing cable (e.g., in thetime domain and/or spatial domain) corresponding to the heating/coolingpulse at the plurality of sensor locations on the optical fiber sensorarray can be measured to support a variety of techniques in accordancewith the disclosed subject matter.

Generally, for purpose of illustration and not limitation, thermalproperties, such as material density, thermal conductivity, heatcapacity, or heat diffusion coefficient, of one or more materials can bemeasured by generating a heat disturbance and sensing a temperatureresponse. In like fashion, dynamic physical properties, such as the flowof a material, can also be measured. As disclosed herein, techniques formeasuring temperature can include obtaining temperature measurements inboth the temporal and spatial domain. For example, distributedtemperature sensing (DTS) systems can provide temperature measurementsalong the length of a sensing cable continuously or at regularintervals. The change in these temperature measurements can correspondto certain properties of a surrounding material or materials.

For purpose of illustration, and not limitation, an exemplary system formeasuring the characteristics of a material in accordance with anexemplary embodiment of the disclosed subject matter will be described.In general, with reference to FIG. 1A, an exemplary sensing system inaccordance with the disclosed subject matter can include a sensing cable101 having disposed therein a heating/cooling device 103 and opticalfiber sensor array having a plurality of sensors 102. The sensing cable101 can be operatively coupled with a control unit 106. For example, theheating/cooling device 103 can be coupled with an excitation source 105,which in turn can be coupled with the control unit 106. Likewise, theoptical fiber sensor array 102 can be coupled with a signal interrogator104, which can be coupled with the control unit 106. Generally, uniformheat can be delivered (e.g., heat energy can be provided or absorbed)along the sensing cable 101 via the heating/cooling device 103 and theexcitation source 105. A temperature profile or its variation with time(e.g., variation rate) can be measured using the optical fiber sensorarray 102 and signal interrogator 104. The control unit 106 can beadapted to collect data, process data, and/or present data forvisualization, for example via one or more displays (not shown).

The sensing cable 101 can be arranged in a variety of configurations.Two exemplary configurations are depicted in FIG. 1B and FIG. 1C,respectively. For example, FIG. 1B depicts a cross section of a sensingcable 101 with the heating/cooling device 103 and the optical fibersensor array 102 arranged in parallel with each other. The sensing cable101 can include, for example, an outer casing (not shown) optionallyfilled with a filler material 110 to maintain the heating/cooling device103 and optical fiber sensor array 102 in place. Additionally oralternatively, the filler can be extended about the heating/coolingdevice 103 and temperature sensor 102 with or without the outer casing.The filler can be, for example, a material with high thermalconductivity, such as magnesium oxide (MgO). The outer casing can be arigid and/or durable material, for example a metal tube. To ensuremeasurement accuracy, e.g., under harsh conditions, such as corrosion,the sensing cable 101 casing can be treated with a suitable coating, asdescribed in more detail below. Alternatively, and as depicted in crosssection in FIG. 1C, the heating/cooling device 103 and the temperaturesensor array 102 can be generally coaxial with each other, wherein theheating/cooling device 103 is disposed concentrically around thetemperature sensor array 102.

As embodied herein, the sensing cable 101 can be mineral insulated forprotection of a optical fiber sensor array 102 including one or moreoptical fibers. The optical fibers can be coated and placed into aprotective tube structure for enhanced mechanical integrity andresistance to adversary effects of environmental factors, such as H₂,H₂S and moisture. The sensing cable 101 can further be protected usingmetal and mineral insulation material (e.g., MgO) for effective thermalconduction. The optical fibers can have a relatively small diameter, andthus can be placed into a protective tube with a relatively smalldiameter, allowing a faster thermal response and dynamic processmonitoring. One of ordinary skill in the art will appreciate that thedimensions of the sensing cable 101 can be selected for a desiredapplication. For example, if further protection from the localenvironment is desired, a sensing cable 101 with a larger diameter, andthus additional filler, can be selected.

Furthermore, a number of commercially available fibers for thetemperature sensor 102 can be used, such as a Fiber Bragg Grating array,Raman scattering based sensor, Rayleigh scattering based sensor orBrillouin scattering based sensor. One of ordinary skill in the art willappreciate that each type of fiber sensor can have certain properties,such as response time, sensing resolution, immunity to hydrogendarkening, effective sensing cable length, and ability to sensetemperature and/or strain, as illustrated for purpose of example and notlimitation in Table 1. For example, a Fiber Bragg grating sensing systemcan include a relatively fast response time, high spatial resolution,and can be employed over a sensing cable length upwards of 100 km orlonger in connection with the use of optical fiber amplifiers. Raman andBrillouin scattering sensing systems can have relatively low responsetimes (e.g., on the order of several seconds), and spatial resolution onthe order of centimeters. Rayleigh scattering sensing systems, whenoperated to sense temperature, can have a response time of severalseconds with relatively high spatial resolution.

TABLE 1 Fastest Typical Immunity response point sensor to H2 Longestsensor Sensor types time size (m) darkening cable length Fiber Bragg <10ms 0.01 high <100 km or Grating (FBG) longer Raman >Several 0.25~0.5 low<100 km scattering sensor seconds Rayleigh >Several 0.01 low  <70 mscattering sensor seconds (Temp) Rayleigh  <1 ms 0.5  low <100 kmscattering sensor (Acoustic) Brillouin >Several  0.1~50 low <100 kmscattering sensor seconds

One of ordinary skill in the art will also appreciate that certain ofthe various types of sensing systems can be used to sense temperatureand/or strain (e.g., to sense acoustics). For example, Fiber BraggGrating sensing systems can be used to measure both temperature andstrain, for purposes of sensing temperature and acoustics. Ramanscattering sensing systems are typically used to sense temperature.Brillouin scattering sensing systems can be used to measure temperatureand strain, and are typically used to sense temperature. Rayleighscattering sensing systems can be used to measure temperature andstrain, and can be used to sense either temperature or acoustics. One ofordinary skill in the art will appreciate that when Rayleigh scatteringsensing systems are used to sense acoustics, response time can increaseto lower than 1 ms and spatial resolution can increase to approximately50 cm.

Referring again to FIG. 1A, and as noted above, the control unit 106 canbe coupled with the signal interrogator 104. The signal interrogator 104can be, for example, an optical signal interrogator. Various opticalsignal interrogators may be used, depending on the type of optical fibersensing techniques to be employed. The controller 106 can be adapted toperform signal processing on real-time temperature data provided by thesignal interrogator 104. For example, the control unit 106 can beadapted to identify and record continuous or repeated temperaturemeasurements at each of a plurality of sensor locations along thesensing cable 101. Additionally, the control unit 106 can be adapted toprocess temperature measurements over time to identify a characteristicof the material surrounding the sensing cable at one or more sensorlocations.

As disclosed herein, a variety of suitable methods can be employed forgenerating the heating/cooling pulse along the sensing cable 101. Asused herein, the term “pulse” includes a waveform of suitable shape,duration, periodicity, and/or phase for the intended purpose. Forexample, and not limitation, and as described further below, the pulsemay have a greater duration for one intended use, such as thedetermination of deposits, and a shorter duration for another intendeduse, such as the determination of flow. As embodied herein, theheating/cooling device 103 can be an electrically actuated device. Forexample, the heating/cooling device 103 can include a resistive heatingwire, and the excitation source 105 can be electrically coupled with theheating wire and adapted to provide a current there through. Passing ofa current through the resistive heating wire can provide thermal energyalong the length of the sensing cable 101, thereby generating a uniformheating/cooling effect along the sensing cable. Alternatively, theheating/cooling device 103 can include a thermoelectric device, and canbe likewise coupled to the excitation source 105. The thermoelectricdevice can use the Peltier effect to heat or cool a surrounding medium.That is, for example, the thermoelectric device can be a solid-stateheat pump that transfers heat from one side of the device to the other.The thermoelectric device can be configured, for example, to provideheating to the optical fiber sensor for a certain polarity of electricpotential and cooling for the opposite polarity. As disclosed herein,and for purpose of simplicity, the terms “heating/cooling device”, and“heating/cooling pulse” will be referred to generally as a “heatingdevice” or “heating element” and as a “heat pulse,” respectively.Depending upon the context, such terms are therefore understood toprovide heating, cooling, or both heating and cooling.

In an exemplary embodiment of the disclosed subject matter, theexcitation source 105 can be configured to deliver current in apredetermined manner. For example, the excitation source 105 can beconfigured to generate pulses having predetermined wave forms, such assquare waves, sinusoidal waves, or saw tooth waves. The excitationsource 105 can be configured to generate the pulses at a predeterminedfrequency. For example, and not limitation, and with reference to FIG.2, the excitation source 105 can be configured to generate an electricpulse of a rectangular wave form 210 through the heating/cooling element103. The electric pulse can create a heat pulse 220 in theheating/cooling element 103 with the same wave form. That is, forexample, the heat flow through the heating/cooling element 103 can begiven by I²R/A, where I is the current, R is the resistance of theheating/cooling element 103, and A is the surface area of a crosssection of the heating/cooling element 103. The heat pulse can result ina heat exchange between the sensing cable 101 and the surrounding media.The temperature at each sensor location can be recorded to generate a“temperature profile” 230 for each sensor location. For example, thetemperature at each sensor location can be recorded with a samplingfrequency of 50 Hz. The temperature profile 230 can correspond tocharacteristics of the medium surrounding the sensing cable 101 at eachsensor location.

For purposes of illustration, and not limitation, the underlyingprinciples of thermally activated (“TA”) measurement techniques will bedescribed generally. Prior to heating or cooling by the heating/coolingdevice 103, temperature measurements of the surrounding medium can betaken with the optical fiber sensor array 102 of the sensing cable 101and the temperature profile can be recorded as a reference. Due to theJoule effect, the heating device 103 can deliver a constant and uniformheat along the cable, heating up both cable and surrounding medium nearthe cable surface. For purposes of illustration, the temperaturemeasured by the optical fiber can be described by the followingequation:

$\begin{matrix}{{\frac{\partial T}{\partial t} = {\frac{1}{{mc}_{p}}( {{\overset{.}{E}}_{gen} - {\overset{.}{E}}_{loss}} )}},} & (1)\end{matrix}$

where Ė_(gen) is the heat generation rate per unit length from theheating device, Ė_(loss), is the heat loss rate due to heat transferfrom the sensing cable to the surrounding medium, and m and c_(p)represent the mass and heat capacitance of the sensing cable per unitlength. The heat generation within the sensing cable due to the Jouleeffect can be given by:

Ė _(gen) ∝Zi ².  (2)

where Z is the impedance of the sensing cable per unit length and therate of heat loss from the sensing cable to the surrounding media can bedecomposed into heat diffusion and heat convection (e.g., Ė_(loss) caninclude both heat diffusion (conduction) in a stationary medium and orconvective heat transfer in a flowing medium):

Ė _(loss) =Ė _(diffusion) +Ė _(convection)  (3)

For a stationary medium, the heat loss term can be given as:

Ė _(loss) ∝AkΔT,  (4)

where A is effective heat transfer area of the sensing cable, k iseffective heat conduction coefficient of the medium and ΔT is theeffective temperature gradient across the sensing cable and the medium.

The heat capacitance of the cable per unit length can limit thefrequency of the thermal response of the cable, and thus the cable canbe designed with a heat capacitance suited to the desired datafrequency. Because heat generation can be relatively constant anduniform, the rate of change in localized temperature can dependprimarily on the heat transfer between the cable and the surroundingmedium. If the localized heat transfer is high at a particular point onthe sensing cable, then the rate of change of temperature at that pointalong the cable, measured by one temperature sensor in the opticalfiber, can be small. Otherwise, the temperature changing rate will belarge. When subject to a heterogeneous medium or a mixed mediumconsisting of layers of different fluids or the like, the spatialdistribution of the temperature along the sensor array can be indicativeof the interface between the different media.

For purpose of illustration, and not limitation, transient temperatureanalysis techniques to determine characteristics of a medium will now bedescribed with the sensing cable modeled as an infinitely long thincylinder placed in an infinite homogeneous medium. For purposes of thisdescription, it is assumed that at time zero (t=0) an electricalcurrent, i, and the heat generation rate per length of the cylinder isgiven by:

q=πr ₀ ² z ₀ i ²,  (5)

where r₀ is the radius of the cylinder, and z₀ is the resistance of thecylinder per unit of volume. A closed form solution for the temperatureon the surface of the cylinder can be given as:

$\begin{matrix}{{{T( {r_{0},t} )} = {T_{\infty} = {\frac{q}{4\pi \; k}{\int_{\frac{r_{0}^{2}}{4\alpha \; t}}^{\infty}{\frac{^{- u}}{u}\ {u}}}}}},} & (6)\end{matrix}$

where k and α are the heat conductivity and diffusivity coefficients ofthe medium, and T_(∞) is the initial temperature distribution along thesensing cable. The normalized temperature change and normalized time tcan be defined as:

$\begin{matrix}{{{\Delta \; T^{*}} = \frac{{T( {r_{0},t} )} - T_{\infty}}{q/( {4\pi \; k} )}}{and}} & (7) \\{t^{*} = {\frac{4\alpha \; t}{r_{0}^{2}}.}} & (8)\end{matrix}$

Equation 6 can thus be given as:

$\begin{matrix}{{\Delta \; T^{*}} = {\int_{1/t^{*}}^{\infty}{\frac{^{- u}}{u}\ {{u}.}}}} & (9)\end{matrix}$

The incomplete gamma function can have following expansion form forsmall but non-zero value of z (0<z<2.5):

$\begin{matrix}{{\Gamma (z)} = {{\int_{z}^{\infty}{\frac{^{- u}}{u}\ {u}}} = {{- \gamma} - {\ln (z)} - {\sum\limits_{n = 1}^{\infty}\; {\frac{( {- z} )^{n}}{n( {n!} )}.}}}}} & (10)\end{matrix}$

The temperature response as given by equation 6 above can be furtherapproximated as

ΔT*≈−γ−ln(1/t*),  (11)

when

z=1/t*<<1.  (12)

In accordance with this illustrative and non-limiting model, comparisonof the normalized temperature change as a function of normalized time(e.g., as given by equation 9 and equation 11, respectively) indicatesthat when the normalized time is greater than approximately 10, equation11 is a good approximation of normalized temperature change. Moreover,equation 11 above indicates that temperature change can increaselinearly with the log of time when the heating time is sufficientlylarge so as to satisfy the criteria in equation 12. Thus, the equationcan be written as:

ΔT(r ₀ ,t)≈a+b ln(t),  (13)

where parameters a and b are function of thermal properties of themedium for given heating rate, and are given by:

$\begin{matrix}{{a = {\frac{q}{4\pi \; k}( {{- \gamma} - {\ln ( \frac{r_{0}^{2}}{4\alpha} )}} )}}{and}} & (14) \\{b = {\frac{q}{4\pi \; k}.}} & (15)\end{matrix}$

Thus, equation 13 can provide a theoretical basis for determining thethermal properties of a medium based on measurement of transienttemperature. One of ordinary skill in the art will appreciate thatcontinuous heating can consume more electrical energy and makemeasurements less sensitive to dynamic change of the thermal propertiesto be measured (e.g., when the medium mixture changes with time), andthus pulsed heating in accordance with the disclosed subject matter canprovide benefits such as decreased electrical energy usage and formeasurement of dynamic conditions of surrounding materials.

For purpose of illustration, and not limitation, an exemplary method ofmeasuring the characteristics of the media surrounding the sensing cableusing thermal analysis sensing techniques will be described. In general,an optimized waveform of electrical pulse (for example, a square wave)can be delivered along the length of the heating/cooling device 103, andtemperature can be monitored using a temperature sensor array 102, e.g.,optical fiber sensors. Owing to the uniformity of the heating/coolingeffect along the sensing cable, temperature readings can vary dependingon localized heat transfer process, which can be a function of thethermal properties (e.g., thermal conductivity, heat capacity) andphysical conditions (static or flow) of the medium surrounding thesensing cable 101. The control unit 106 can be adapted to determine thecharacteristics of the surrounding media simultaneously, using thetemperature profile.

A single heating pulse (e.g., arising from an optimized waveform ofelectrical pulse) can create a temperature response which can be derivedin accordance with the exemplary and non-limiting model described hereinusing superposition as follows:

$\begin{matrix}{{{T( {r_{0},t} )} - T_{\infty}} = {\frac{q}{4\pi \; k}{( {{\int_{\frac{r_{0}^{2}}{4\alpha \; t}}^{\infty}{\frac{^{- u}}{u}\ {u}}} - {\int_{\frac{r_{0}^{2}}{4{\alpha {({t - t_{0}})}}}}^{\infty}{\frac{^{- u}}{u}\ {u}}}} ).}}} & (16)\end{matrix}$

The first term in the bracket of equation 16 can represent the heatingfrom t to t₀, and the 2nd term the cooling after t₀. Data collectedduring heating and cooling are analyzed separately, as disclosed herein,to derivate estimates of thermal properties of the medium.

Based upon the above, the control unit 106 can be adapted to determinethe characteristics of the surrounding media using a variety of suitabletechniques. For example, the temperature profile at each sensor locationcan be used to determine the characteristics of the surrounding mediadirectly. The temperature measurements during heating and/or cooling ofthe sensing cable, corresponding to the timing of the rectangularelectrical pulse, can be used to generate a feature-temperature profileat each sensor location. For example, the feature-temperature profilescan be extracted from the temperature data at distinctive conditions:heating (e.g., the condition during which the heat pulse is passing overa sensor location), cooling (e.g., the condition during which the heatpulse has passed over the sensor location and heat is being exchangedbetween the sensing cable and the surrounding media) and peaktemperature (e.g., approximately the maximum temperature recorded at thesensor location for each heat pulse).

For purpose of illustration, and not limitation, and with reference toFIG. 3, the control unit 106 can be configured to determine temperaturecharacteristics of surrounding media using the feature-temperatureprofile at each sensor location. FIG. 3 shows distribution of featuretemperatures along a sensing cable surrounded by different media atdifferent sensor locations. Graph 330 depicts the measured temperatureprofiles for a plurality of sensor locations. In accordance with thedisclosed subject matter, feature-temperatures 331 b, 332 b, and 333 bcan be extracted from the measured temperature profile depicted in graph330. For example, at each sensor location, feature-temperature 331 b cancorrespond to a heating condition (e.g., while the heat pulse is passingover the sensor location), and can be extracted for each sensor locationat a corresponding time 331 a. Likewise, feature-temperature 332 b cancorrespond to a peak temperature, and can be extracted for each sensorlocation at a corresponding time 332 a. Similarly, feature temperature333 b can correspond to a cooling condition (e.g., after the heat pulsehas passed over the sensor location and during which heat exchangebetween the cable and the surrounding media takes place) and can beextracted for each sensor location at a corresponding time 333 a.Temperature 310 is the measured temperature at each sensor locationduring ambient conditions (e.g., no heat is applied).

As illustrated by FIG. 3, the feature temperature at each sensorlocation can correspond to the temperature characteristics of thesurrounding media. For example, as depicted in FIG. 3, a 36 inch sensingcable arranged in a vertical configuration with a sensor disposed orlocated each unit inch along the cable can be exposed to a stack of air,oil, emulsion, and water. It should be noted that FIG. 3 depicts datafrom 24 sensor locations. Assuming each medium is stationary around thesensing cable, the rate of heat exchange, and thus thefeature-temperature profiles 331 b, 332 b, and 333 b, between thesensing cable and the surrounding media at each sensor location cancorrespond to the heat conduction of the surrounding media. That is, forexample, heat transfer between the sensing cable and surrounding air canbe lower than that between the sensing cable and water, as water has ahigher heat conduction. Oil and emulsion layers can also be identifiedin this manner.

The determination of the characteristics of the media surrounding thesensing cable can be achieved by further configuring the control unit106 to process the temperature profile. For example, in accordance withan exemplary embodiment of the disclosed subject matter, the regressionof the temperature over log of time can be performed over an interval oftime corresponding to each heat pulse for each sensor location. Theslope and intercept of the regression can be used to identify thematerial characteristics. For example, the regression can take thefunctional form of T=b+m ln(t), where T is the temperature measurement,ln(t) is the natural log of the time of the temperature measurement, bis the intercept of the regression, and m is the regression coefficient.

The interval over which the regression is taken can be, for example,during the heating condition described above (e.g., during which theheat pulse passes over the sensor location). Because heating can occurin a logarithmic manner, taking the regression as a function of the logof time and provide for results with lower error (e.g., a highercorrelation coefficient). That is, for example, the temperature as afunction of the log of time can be substantially linear over the heatingperiod. Alternatively, the interval over which the regression is takencan be during the cooling condition described above. For purpose ofillustration, and not limitation, for a square electrical pulse from 0current to a constant non-zero value, the constant non-zero currentvalue can correspond to the heating stage, and zero current cancorrespond to the cooling stage. The slope of the regression for theheating stage can be computed over a fraction of pulse duration when thecurrent is non-zero, while slope of the regression for the cooling stagecan be computed over a fraction of the time for which the currentchanges to zero value. Additionally or alternatively, the regression cantake a number of suitable functional forms. For example, an nth orderpolynomial regression can be taken if the functional form of thetemperature profile resembles an nth order polynomial.

For purpose of illustration, FIG. 4A shows the regression results of onetemperature measurement at a sensor location in each material of FIG. 3.Line 420 corresponds to a plot of temperature at a sensor location inoil over the log of time. Likewise, lines 430, 440 and 450 correspond toa plot of temperature at a sensor location in air, emulsion, and water,respectively, over the log of time. Regression can be performed over aregression interval 410, which can correspond to the heating conditionof the respective temperature sensor. The results of the regression canbe plotted. For example, line 421 is a plot of the regression of line420. As illustrated by FIG. 4A, the slope and intercept of eachregression can correspond to a characteristic of the surroundingmaterial, and such characteristics can be determined. That is, withreference to FIG. 4A, each material having different thermalcharacteristics can have a different slope and intercept, and can thusbe identified. As depicted in FIG. 4A, the deviations in measurementsresulting from the linear fitting line after the regression interval, asshown by line 420 and line 421, can be due to boundary effects from thewall of the vessel. One of ordinary skill in the art will appreciatethat the description of the underlying principles herein assumes thethermal energy delivered by the sensing cable diffuses out without anyboundaries. However, in the presence of such boundaries, thermal energywill be contained in a finite space and eventually thermal equilibriumwill be reached. Accordingly, the regression interval can be selectedbased on a desired application, including corresponding boundaryconditions.

For purpose of illustration, FIG. 4B shows the regression results for 24temperature sensors of FIG. 3, showing both slopes 450 and intercepts470. As illustrated by FIG. 4A and FIG. 4B, in certain circumstancesthese techniques can provide determination of material characteristicswith reduced error, comparing results from FIG. 4B with FIG. 3 todifferentiate the emulsion layer and the oil layer. The interval overwhich the regression can be performed can be predetermined to reduceboundary effect errors (e.g., error 422 induced by boundary effects inthe plot of line 420). That is, for example, taking the regression overa small interval can omit certain features of a temperature profile thatcan correspond to a particular characteristic. Accordingly, theregression interval can be predetermined such that errors induced byboundary effects are reduced. For example, the regression interval canbe predetermined by calibration and/or with reference to knownparameters or operating conditions of the system, such as expectedfeatures of a temperature profile.

In accordance with another aspect of the disclosed subject matter,enhanced determination of the characteristics of media surrounding thesensing cable can be achieved with a control unit 106 configured toprocess the temperature profile in the frequency domain. A N-pulse train(i.e., application of a certain periodic form of current through thesensing cable to generate N cycles of heating and cooling) can bepropagated through the heating/cooling element 103. The period of aheating/cooling cycle, t₀, the number of heating cycles, N, and thecurrent amplitude, I₀, can be selected. The heating/cooling pulses canbe applied to the heating/cooling element 103 with the excitation source105 to generate thermal excitation within the sensing cable 101.

Temperature readings from the optical fiber sensor array 102 can becollected via the signal interrogator 104 at a selected samplingfrequency. The sampling frequency can be, for example, at least twicethe maximum signal frequency of interest. A temperature series,T_(i)(1), T_(i)(2), T_(i)(3), . . . can be generated where i=1, 2, 3, .. . M, is the sensor index. In accordance with certain embodiments,synchronized sampling techniques can be employed to reduce the samplenumber, increase the signal to noise ratio, and improve Fouriertransform accuracy. The time difference of the temperature readingsΔT=[T(k+1)−T(k)]/Δt, can be calculated using the control unit 106 togenerate time series of temperature derivative ΔT_(i)(1), ΔT_(i)(2),ΔT_(i)(3) . . . , where sensor index i=1, 2, 3 . . . M. In connectionwith the following description, the temperature difference, differencedtemperature, or temperature derivatives are all referred to as the timeseries ΔT′. A transform (e.g., a Fast Fourier Transform [FFT], orDiscrete Fourier Transform [DFT]) can be applied, using the control unit106, to generate a spectrum of time series of temperature difference forM sensors. For each sensor, the real and imaginary values of thespectrum at fundamental frequency of N-Pulse train can be selectedf₀=1/t₀. The characteristics of the surrounding media can thus bedetermined as disclosed herein using M pairs of the values derived fromthe spectrum of the temperature difference as described above.Alternatively, the frequency differenced spectrum (i.e., obtained byapplying the operation of taking the derivative of the spectrum oftemperature difference with respect to the frequency) and the real andimaginary values of the differenced spectrum can be used. Thecharacteristics of the surrounding media can thus be determined asdisclosed herein using M pairs of the values derived from thedifferenced spectrum as described above.

That is, for example, the time derivative of the temperature data can bedetermined (i.e., resulting in the differenced temperature). The Fouriertransform of the time-derivative temperature can then be determined, andthe derivative of the complex spectrum with respect to the frequency canbe calculated (i.e., resulting in the differenced spectrum). Theamplitude and phase of the frequency-derivative spectrum (differencedspectrum) can then be calculated. The amplitude and phase of thefrequency-derivative spectrum can correspond to the characteristics ofthe surrounding media at each sensor location. For purpose ofillustration, FIG. 5B shows the phase of the frequency-derivativespectrum of the temperature measurements over the sensor locations asillustrated in FIG. 3. Likewise, FIG. 5C shows the amplitude of thefrequency-derivative spectrum of the temperature measurements over thesensor locations as illustrated in FIG. 3. As illustrated by thefigures, the techniques disclosed herein can provide for enhancedaccuracy in the measurement and differentiation of the levels andinterfaces between the air, oil, emulsion, and water layers.

As embodied herein, the sensing cable 101 can be calibrated, e.g., withthe control unit 106. Calibration can include calibrating the sensorarray to ensure that each sensor at a different location along thesensing cable provides the same output when subject to the same materialof a constant thermal property. For example, the sensing cable 101 canbe submerged into a homogenous medium of known thermal property, and thetemperature measurements and processing techniques disclosed herein canbe applied. If there is a difference between sensor output, thedifference can be used as compensation and can be applied duringmeasurements. Additionally, calibration can include ensuring that thesensor output accurately estimates the particular characteristic ofinterest (e.g., thermal conductivity and/or diffusivity). For example, anumber of materials with known thermal properties can be measured for abroad range of values and a database can be constructed includingcorrelations between measurements and determined characteristics of theknown materials. The database can then be used to interpolate a measuredcharacteristic of an unknown material.

For purpose of illustration, and not limitation, the underlying theoryof measurement techniques in accordance with this exemplary embodimentwill be described. In connection with this description, for purpose ofexample, the waveform of the pulse train propagated through the heatingdevice can be a square shape current, e.g., as illustrated in FIG. 2.The current can be defined mathematically as:

$\begin{matrix}{{{i(t)} = {\sum\limits_{n = 1}^{N}\; {\{ {{H( {t - {( {n - 1} )t_{0}}} )} - {H( {t - {( {n - \frac{1}{2}} )t_{0}}} )}} \} I_{0}}}},} & (17)\end{matrix}$

where t₀ is the period, I₀ is the amplitude of the current, and Hdenotes the Heaviside step function defined by:

$\begin{matrix}{{H( {x - x_{0}} )} = \{ {\begin{matrix}0 & {x < x_{0}} \\1 & {x \geq x_{0}}\end{matrix}.} } & (18)\end{matrix}$

The heating rate can thus be given as:

$\begin{matrix}{{{q(t)} = {\sum\limits_{n = 1}^{N}\; {\{ {{H( {t - {( {n - 1} )t_{0}}} )} - {H( {t - {( {n - \frac{1}{2}} )t_{0}}} )}} \} q_{0}}}},} & (19)\end{matrix}$

where q₀ is related to the current by equation 5.

Instead of analyzing the temperature in time domain, the temperaturerate, i.e., the derivative of the temperature with respect to time, canbe considered in the frequency domain. The derivative operation, ahigh-pass filtering, can remove the slow-varying trend of thetemperature for easier analysis. The time derivative of the temperatureand heating generation rate can be defined as follows:

$\begin{matrix}{{{\overset{.}{T}( {r,t} )} = \frac{T}{t}}{and}} & (20) \\{{\overset{.}{q}(t)} = {\frac{q}{t}.}} & (21)\end{matrix}$

In frequency domain, the counterparts to the temperature and heatinggeneration rate can be complex spectrum functions of S(r,ω) and Ω(ω).For large distances away from the heating element, the thermal diffusionprocess can exhibit the behavior of an attenuated and dispersive wave.The complex spectrum of the change rate of the temperature on thesensing cable's surface can be given as:

$\begin{matrix}{{S( {r_{0},\omega} )} = {\frac{1}{2\pi \; k}\frac{\Omega (\omega)}{\kappa \; r_{0}}{\frac{H_{0}^{(2)}( {\kappa \; r_{0}} )}{H_{1}^{(2)}( {\kappa \; r_{0}} )}.}}} & (22)\end{matrix}$

The contribution of the heating component, Ω at a center frequency of ω,to the change rate of the temperature on the sensing cable's surface canthus be given as:

d{dot over (T)}(r ₀ ,ω,t)=S(r ₀,ω)e ^(jωt) dω.  (23)

Integration of above over all frequencies can recover the temperaturerate in time domain. Therefore, S can be used as indicator of themedium. For purpose of illustration, and not limitation, the excitationterm, Ω will now be described in greater detail. From equations 19 and21, the derivative of the heating generation can be given as:

$\begin{matrix}{{\overset{.}{q}(t)} = {\sum\limits_{i = 1}^{N}\; {\{ {{\delta ( {t - {( {i - 1} )t_{0}}} )} - {\delta ( {t - {( {i - \frac{1}{2}} )t_{0}}} )}} \} q_{0}}}} & (24)\end{matrix}$

in time domain, and:

$\begin{matrix}{{\Omega (\omega)} = {{q_{0}( {^{{j\omega}\; t_{0}} - ^{j\frac{\omega \; t_{0}}{2}}} )}{\sum\limits_{n = 1}^{N}\; ^{j{({n\; \omega \; t_{0}})}}}}} & (25)\end{matrix}$

in frequency domain. Because N is finite, Ω can contain all frequencies.The components at the harmonic frequencies can be given as:

$\begin{matrix}{{\omega_{k} = {{k\; \omega_{0}} = {k\frac{2\pi}{t_{0}}}}},} & (26)\end{matrix}$

with index k.

Evaluation of equation 25 at the harmonic frequencies gives:

$\begin{matrix}{{\Omega ( \omega_{k} )} = \{ {\begin{matrix}{2\; {Nq}_{0}} & {{k = 1},3,{5\mspace{14mu} \ldots}} \\0 & {{k = 0},{24\mspace{14mu} \ldots}}\end{matrix}.} } & (27)\end{matrix}$

As such, Ω peaks at odd harmonics but zeros at even harmonics. Atnon-harmonic frequencies, Ω is complex in general. FIG. 5A depicts anexemplary plot of Ω/q₀ verse ω/ω₀ for N=1, 2, or 3. Accordingly, thethermal excitation energy can be concentrated at odd harmonics offundamental frequency of pulses and increase as N increases.

As embodied herein, one of the odd harmonic frequencies can be chosen toincrease signal to noise ratio in analysis of temperature measurements.In this manner, any temperature variation introduced by non-electricalheating can introduce noise which could be difficult to handle in timedomain but can be reduced in frequency domain via N-pulse train: thenumber of cycles, N, can be increased to boost the peak value at oddharmonics. Additionally or alternatively, synchronized samplingtechniques or harmonic tracking can also be used to reduce the noise.

In accordance with an exemplary embodiment, the spectrum S(ω), e.g., asgiven in equation 22, can be used to estimate the thermal property of amedium surrounding the sensing cable. A characteristic frequency can begiven as:

$\begin{matrix}{\omega^{*} = {\frac{\alpha}{r_{0}^{2}}.}} & (28)\end{matrix}$

The complex argument to the Hankel functions can thus become:

$\begin{matrix}{{{\kappa \; r_{0}} = {{\sqrt{{- j}\frac{\omega}{\alpha}}r_{0}} = {\sqrt{\frac{\omega}{\omega^{*}}}^{j\theta}}}},} & (29)\end{matrix}$

Where θ=3/4π for ω>0. At low frequencies where ω/ω* (amplitude of κτ₀)is less than 1, the Hankel functions can be approximated as:

$\begin{matrix}{{{H_{0}^{(2)}( {\kappa \; r_{0}} )} \approx {1 - \frac{( {\kappa \; r_{0}} )^{2}}{4} - {j\frac{\pi}{2}{\ln ( {\kappa \; r_{0}} )}}}}{{and}\text{:}}} & (30) \\{{H_{1}^{(2)}( {\kappa \; r_{0}} )} \approx {\frac{\kappa \; r_{0}}{2} - \frac{( {\kappa \; r_{0}} )^{3}}{16} + {j\frac{2}{\pi}{\frac{1}{\kappa \; r_{0}}.}}}} & (31)\end{matrix}$

The spectrum, S, can thus reduce to:

$\begin{matrix}{{{S( {r_{0},\omega} )} = {\frac{\Omega}{2\pi \; k}{\hat{X}( \frac{\omega}{\omega^{*}} )}}},} & (32)\end{matrix}$

where the normalized transfer function, and temperature change responseto the thermal excitation Ω/2πk at frequency ω/ω* can be given as:

$\begin{matrix}{{{\hat{X}( \frac{\omega}{\omega^{*}} )} = {( {R_{s} + {j\; I_{s}}} ) = {X\; ^{j\varphi}}}},} & (33) \\{{R_{s} \approx \frac{{\frac{1}{32}( \frac{\omega}{\omega^{*}} )^{2}} + {\frac{1}{2\pi}\frac{\omega}{\omega^{*}}} + {\frac{1}{2\pi}( {\frac{\omega}{\omega^{*}} - \frac{4}{\pi}} ){\ln ( \frac{\omega}{\omega^{*}} )}}}{{\frac{1}{4}( \frac{\omega}{\omega^{*}} )^{2}} - {\frac{2}{\pi}( \frac{\omega}{\omega^{*}} )} + \frac{4}{\pi^{2}}}},{and}} & (34) \\{{I_{s} \approx \frac{{\frac{5}{4}( {\frac{\omega}{\omega^{*}} - \frac{4}{\pi}} )} - {\frac{1}{16\pi}( \frac{\omega}{\omega^{*}} )^{2}{\ln ( \frac{\omega}{\omega^{*}} )}}}{{\frac{1}{4}( \frac{\omega}{\omega^{*}} )^{2}} - {\frac{2}{\pi}( \frac{\omega}{\omega^{*}} )} + \frac{4}{\pi^{2}}}},} & (35)\end{matrix}$

after neglecting terms of higher order.

As disclosed herein, and in accordance with an exemplary embodiment ofthe disclosed subject matter, the amplitude and phase can decreasemonotonically with frequency so that higher frequency corresponds withlower response of temperature to the heating. Accordingly, lowerfrequencies can obtain significant heating response and higher signals.Additionally, the imaginary part of the complex spectrum can be nearlylinear with the frequency while the real part can exhibit linearbehavior beyond certain frequency values. Therefore, the derivative ofthe transfer function spectrum with respect to frequency can lead toconstants beyond certain values of ω/ω*. One of ordinary skill in theart will appreciate that, mathematically, the spectral derivative isequivalent to the Fourier transform of the temperature rate with respectto the log of time. Thus there is connection of the derivative spectrumwith the linear relationship of the temperature change with log(t) inthe time domain as shown in equation 13.

As embodied herein, systems and methods in accordance with the disclosedsubject matter include detecting a deposit in a vessel with a sensingcable including an optical fiber sensor array aligned with aheating/cooling element. The method includes propagating at least oneheating/cooling pulse through the heating/cooling element along at leasta portion of the sensing cable to affect an exchange of thermal energybetween the heating element and one or more media exposed to the sensingcable. The method includes measuring, over time, a temperature profileof the sensing cable corresponding to the heat pulse at each of aplurality of sensor locations on an optical fiber sensor array. Themethod includes detecting a deposit by determining one or moreproperties of the materials exposed to the sensing cable at each of theplurality of sensor locations based on the temperature profilecorresponding thereto.

For purpose of illustration and not limitation, reference is made to theexemplary embodiments of FIG. 1. The method and system disclosed hereincan be used to detect a variety of types of deposits in any of a numberof components and vessels. For example, formation of deposits such asdebris, bio-growth, inorganic or organic fouling, water condensation,coke, and the like within a component of a refinery can be detectingusing the system and method herein. Such components include, but are notlimited to a vessel of a heat exchanger, a furnace tube, a pipe of aproduction well, a pipeline, a tray or packing material of adistillation tower, a catalytic hydroprocessing reactor, apolymerization reactor, a wash bed in a distillation tower, such as avacuum pipe still (VPS) distillation tower, or the like. In operation,formation of such deposits can cause problems, such as capacity loss,increased operational costs, and increased energy usage. Detection ofthe onset of the formation of deposits within the component at an earlystage can allow for mitigation strategies, such as increasing the flowrate of wash oil to remove coking. If such coking (or coking precursors)can be detected at the early stage of formation, mitigation techniques,such as administering a wash oil, can be effective; wherein in laterstages of coke formation (such as in the formation of “hard coke”)removal of these deposits can be difficult, if not impossible, toachieve with on-line/in-service techniques. Accordingly, the techniquesdisclosed herein can be employed to detect the formation of deposits ina vessel in connection with a refining operation. However, it isrecognized that the system and method herein can be applied to numerousother environments and vessels in which the detection of deposits isbeneficial or desired.

In accordance with this exemplary embodiment, a system for detecting adeposit in a vessel can include the components and features describedherein with reference to FIG. 1A-C. The sensing cable (e.g., sensingcable 101) can further include a coating with an affinity for foulingresembling that of the interior of the vessel. For example, stainlesssteel, protective polymer coatings, or other suitable coatings can beapplied to the sensing cable in connection with detection of deposits incomponents having a fouling affinity similar to that of stainless steelor polymer coatings, respectively. It is recognized that a variety ofsuitable coatings can be employed, the selection of which can depend onthe desired application environment.

Additionally, the sensing cable (e.g., sensing cable 101) can furtherinclude a shield to establish an approximately stationary condition ofthe surrounding media in a region proximate the sensing cable. As usedherein, the term “approximately stationary” can include a staticcondition, or a flow pattern in which energy transferred from thesensing cable to the surrounding media is substantially conductive,rather than convective. Such flow conditions can include steady laminarflow, or an area of turbulent flow (e.g., a plurality of eddies) whereinthe mean flow velocity is approximately stationary. Additionally oralternatively, and as previously described, such a shield can beconstructed to protect the sensing cable from damage due to solids inthe surrounding media.

For purpose of illustration, and not limitation, FIG. 6 provides aschematic depiction of a shield in accordance with an exemplaryembodiment of the disclosed subject matter. With reference to FIG. 6,the shield 710 can have a semicircular or other suitable shape and canbe disposed upstream of the sensing cable 101 to protect and eliminateflow conditions immediately adjacent the sensing cable 730. If the mediasurrounding the sensing cable has, for example, a laminar flow 720, theshield 710 can create an approximately stationary region 730 proximatethe sensing cable 101 such that heat transfer due to convection andother anomalies resulting from flow conditions is reduced. Any of avariety of suitable materials of construction for the shield can beused, depending on surrounding environmental conditions, such ascorrosion and fouling resistant metal or ceramic for high temperatureenvironment or polymer for lower temperature environments. The size ofthe shield can be large enough to protect the sensor and reduceturbulent flow around the sensor. One of ordinary skill in the art willappreciate that a variety of other suitable shield configurations arepossible, and the scope of the disclosed subject matter is not intendedto be limited to the exemplary embodiments disclosed herein.

Using the systems and techniques as disclosed, and suitablemodifications as desired, a method of detecting a deposit in a vessel isprovided and disclosed herein with reference to FIG. 1A through FIG. 5.For purpose of example, and with reference to FIG. 7, the method ofdetecting a deposit in a vessel will be described in connection withcertain exemplary embodiments, wherein the vessel is a VPS distillationtower 810 and the deposit to be detected is coking 825 formed on a washbed 820 of the VPS distillation tower 810. One of ordinary skill in theart will appreciate that the techniques disclosed herein can be appliedin connection with a variety of suitable vessels and deposits, and thedisclosed subject matter is not intended to be limited to the exemplaryembodiments disclosed herein.

With reference to FIG. 7, the method of detecting coking in a vessel 810can include positioning a sensing cable 101 within a wash bed 820 of theVPS distillation tower 810. For example, the sensing cable 101 can bepositioned across a surface of the wash bed 820 such that the sensingcable 101 is aligned perpendicular to an axis of the vessel 810. In thismanner, sensor locations along the sensing cable 101 can correspond tolocations about a cross section of the vessel 810. The sensing cable 101likewise can be positioned and/or arranged in a variety of othersuitable configurations as desired or needed. For example, the sensingcable 101 can be positioned parallel to an axis of the vessel 810 withthe sensor locations along the sensing cable 101 generally correspondingto locations along a vertical axis within the vessel 810, such as alongan inside wall of the vessel 810. Moreover, as shown in FIG. 8, thesensing cable 101 can be arranged in a grid pattern or array, or anyother suitable pattern, about a surface of the wash bed 820 or otherwisewithin the vessel 810. One of ordinary skill in the art will alsoappreciate that more than one sensing cable can be employed. Forexample, as depicted in FIG. 8, a second sensing cable 910, which canalso be positioned in a grid pattern 911 and 912 with a known sensordensity coverage, e.g., one sensor per square foot, can be positioned onan opposite surface of the wash bed 820.

As previously noted, the sensing cable 101 includes a heating/coolingelement 103, such as a heating wire, and an optical fiber sensor array102, as disclosed herein. The optical fiber includes a plurality ofsensing locations along the length of the fiber, such that each sensinglocation corresponds to a position about the surface of the wash bed820. For example, and as previously noted, the optical fiber can includea plurality of sensors along its length and/or a single fiber sensor canbe movable to define a plurality of sensor locations. The optical fibersensor is coupled to an optical signal interrogator 104 to process anoptical signal therein to obtain temperature measurements at each of thesensor locations. The optical signal interrogator 104 can further becoupled to a control unit 106 to process the temperature measurements.

As previously described herein, the heating wire is coupled to anexcitation source 105 adapted to propagate electromagnetic waves (e.g.,current 210) through the heating wire, thereby creating correspondingheat pulses (e.g., heat pulse 220). As the heat pulses propagate throughthe heating wire, heat is exchanged between the heating wire, thesensing cable, and the surrounding media at each sensor location. Thetemperature at each sensor location can be recorded, e.g., via theoptical signal interrogator and control unit, to generate a temperatureprofile for each sensor location. For example, temperature can bemeasured as a function of time at each sensor location along the opticalfiber. The temperature profile at each sensor location generally willcorrespond to the characteristics of the medium surrounding the sensingcable at that sensor location. In this manner, for purpose ofillustration, sensor locations that are in proximity to deposits (e.g.,coking 825) can result in a temperature profiles distinguishable fromsensor locations not in proximity to deposits.

The temperature profile (i.e., the temperature as a function of time ata sensor location) can generally exhibit an increase in temperaturecoinciding with the exposure to the heat pulse at the correspondingsensor location. For purpose of illustration, and not limitation, andwith reference to the laws of thermodynamics, the temperature willgenerally increase over the duration of the heat pulse at a ratecorresponding to the characteristics of the surrounding media, andthereafter decrease as the heat from the heat pulse diffuses into thesurrounding media at a rate corresponding to the characteristics of thesurrounding media. Thus, the temperature profiles for each sensorlocation can correspond to the characteristics of the surrounding media.e.g., via the heat capacity of the particular media. For example, andnot limitation, at a sensing location surrounded by a deposit, such as aregion of coking 825 in the wash bed 820, the heat transfer from theheating wire into the surrounding coke 825 can be relatively low due tothe low heat capacity and low conductance of coke, and thus temperatureis high at this location and shown as a hot spot. By contrast, at asensing location surrounded by other media in the vessel 810, such asvapor or other effluent, the heat transfer from the heating wire intothe surrounding media can be relatively high due to the relativelyhigher heat capacity and higher conductance of the surrounding effluent,and thus temperature is low at this location and is shown as a coldspot.

For purpose of illustration, and not limitation, reference will be madeto examples of the methods disclosed herein with reference to FIGS.9A-C. FIG. 9A, includes an image of a sensing cable 1011, including anoptical fiber sensor array adjacent a heating wire inside a capillarytube, with four solid resid (i.e., coke) deposits (including deposits1012 a, 1012 b, 1012 c and 1012 d or collectively, 1012) located atintervals along the sensing cable 1011. Initially, for purpose ofillustration, the sensing cable 1011 and deposits 1012 herein are atroom temperature. As a heat pulse propagates through the heating wire,heat is exchanged between the heating wire, the sensing cable, thesurrounding air, and the coke deposits 1012. During heating, overalltemperature readings at each sensor location increase, and thetemperature profile reveals the locations and amount of coke deposits.For example, FIG. 9A includes a plot 1013 of temperature (y-axis) versussensor location in meters (x-axis). Plot 1013 includes “dips” in thetemperature profile corresponding to lower temperature regions caused byextra thermal mass from various sizes of coke deposit.

Likewise, FIG. 9B provides an image 1020 of a sensing cable 1021(including a fiber optic sensor array and heating wire) covered withfive high temperature cement deposits (1022 a, 1022 b, 1022 c, 1022 d,and 1022 e [collectively, 1022]). For purpose of demonstration, thesensing cable 1021 is placed in, for example, a furnace tube operatingat approximately 400° C. As a heat pulse propagates through the heatingwire, heat is exchanged between the heating wire, the sensing cable, thesurrounding air, and the cement deposits 1022. FIG. 9B includes a plot1023 of sensor location along the sensing cable 1021 (x-axis) andtemperature change induced by the heating wire in sensing cable 1021(y-axis). Plot 1023 reveals the locations and amount of high temperaturecement deposits, where the “dips” in the temperature profile are lowertemperature regions caused by extra thermal mass from various sizes ofhigh temperature cement. The 0 point on the y-axis of plot 1023represents the furnace operating temperature at 400° C. Heat generatedby the heating wire is delivered to the sensing cable as thermalperturbation to the environmental thermal equilibrium, and the thermalresponse of the sensing cable is used to measure the deposit locationsand sizes. Thus, this sensing mechanism can enable deposit detectionunder various temperature conditions, e.g., ranging from cryogenictemperatures up to over 1000° C.

FIG. 9C depicts an image 1030 of a sensing cable 1031 with a pluralityof resid deposits (including deposit 1032) located at intervals alongthe sensing cable 1031. For purpose of illustration, the sensing cable1031 is immersed in gas oil and under room temperature conditions. Thetechniques disclosed herein are applied, and a plot such as plot 1033 isgenerated. For example, in connection with FIG. 9C, the heat pulse waspropagated as a single heat pulse with a duration of approximately 85minutes. Plot 1033 depicts the sensor location along the sensing cable(x-axis) as a function of time (y-axis) and depicts the temperaturechange induced by the heating wire in sensing cable (z-axis). Asillustrated by plot 1033, the temperature profile reveals the locationsand amount of coke deposits during both heating (e.g., 1˜85 min) andcooling (e.g., 85˜110 min) and cooling processes. The “peaks” in thetemperature profile correspond to higher temperature regions, caused byvarious sizes of coke, as coke is less thermally conductive than gasoil, temperatures around coke deposits are higher during heatingprocess; and also higher during cooling process because of the higherheat capacity of coke.

As disclosed herein, the control unit thus can be adapted to determinethe characteristics of the surrounding media at each sensor locationusing a variety of techniques, and thereby detect deposits, such ascoking, in a vessel, such as a VPS distillation tower. That is, forexample, the control unit can be adapted to determine, with reference tothe known positions of the sensor locations and the correspondingtemperature profiles, a difference in characteristics of the mediumsurrounding each sensor location and thus detect the location of one ormore deposits. In like manner, deposits can be detected by identifying achange in temperature profile between sensor locations.

For purpose of illustration, and not limitation, the direct temperaturemeasurement techniques described above can be used to detect deposits ina vessel. Particularly, and with reference to FIG. 9D, temperatureprofiles can be extracted and processed to determine characteristics ofthe medium surrounding each sensor location. For example, and asdepicted in FIG. 9D, an additional deposit can be detected by comparingthe temperature profile of sensor locations before and after deposition.FIG. 9D shows an image 1050 of the sensing cable in an initialcondition, with a small amount of wax 1051 deposited over a portion ofthe sensing cable. Plot 1052 illustrates the temperature profiles of thesensor locations during the initial condition, measured in accordancewith the method disclosed herein. An additional amount of wax 1061 canbe deposited, as shown in image 1060. Temperature profiles for thesensor locations after deposition can then be measured in accordancewith the techniques disclosed herein, as shown in plot 1062. Thedifferential between the temperature profile measured after depositionof the additional wax 1061 relative the temperature profile measuredduring the initial condition thus can be used to determine the locationof the additional wax 1061, as well as the relative size of theadditional deposition, as shown in plot 1070. Alternative techniques fordetecting size or amount of the deposit also can be used, as describedbelow.

Alternatively, and as described herein with reference to FIG. 4B, alog-time regression technique can be used to determine certaincharacteristics of the medium surrounding each sensor location byfurther processing the temperature profile at each sensor location. Thatis, by performing the regression of the temperature over log of timeover an interval of time corresponding to each heat pulse for eachsensor location, the resulting slope and intercept of the regression canbe used to identify characteristics of the medium. For example, theslope and intercept of sensor locations in proximity to a deposit can bedistinguished from the slope and intercept of sensor locations not inproximity to a deposit.

In accordance with another exemplary embodiment of the disclosed subjectmatter, the frequency spectrum techniques disclosed herein withreference to FIG. 5A-C can be employed to detect deposits, such ascoking 825, within a vessel, such as VPS distillation tower 810, withincreased measurement sensitivity, accuracy, and/or reliability. In thisexemplary embodiment, and as described above, an N-pulse train can bepropagated through the heating wire of the sensing cable 101 withpre-selected parameters, including heating cycle period, to, number ofheating cycles, N, and current amplitude, I₀. The parameters can beselected according to the operating characteristics of the VPSdistillation tower 810 such that the resulting temperature profile canbe measured with a desired signal-to-noise ratio. For example, a longerheating cycle period or higher current amplitude can result in highersignal-to-noise ratio relative to a shorter heating cycle period orlower current amplitude. Likewise, an increase in the number of heatingcycles can further increase the signal-to-noise ratio. One of ordinaryskill in the art will appreciate that such parameters can be varieddepending upon desired application. For example, if detection ofdeposits is desired at short time intervals, a shorter heating cyclerperiod and a higher current amplitude can be employed. For purpose ofexample, and not limitation, in connection with a wash bed 820 in a VPSdistillation tower 810 having a diameter of approximately 20 toapproximately 40 feet, approximately 4 to 5 layers of wash bed packingmaterials, and a total height of approximately 6 to approximately 10feet. The heating cycle period for the sensing cable can beapproximately 1 Hz or slower (i.e., the excitation source can be adaptedto deliver a current pulse at 1 Hz or slower. The current amplitude canbe several mili-amperes to several amperes. One of ordinary skill in theart will appreciate that, in accordance with the disclosed subjectmatter, suitable frequency and current amplitude can be determined for aparticular application by routine testing in accordance with knownmethods.

The optical signal interrogator 104 can be adapted to measuretemperatures from the optical fiber at a pre-selected samplingfrequency. In accordance with an exemplary embodiment, the samplingfrequency can be at least twice the expected frequency of thetemperature profile and/or heat pulse. For example, and not limitation,in connection with a VPS distillation tower 810, the sampling frequencycan be 10 Hz or less. The derivative with respect to time of thetemperature measurements for each sensor location can then be generated.For example, the measured temperatures a sensor location at eachsampling interval can be given as a temperature series. The differencebetween each temperature in the series can then be calculated togenerate a temperature derivative series. A transform (e.g., a FFT orDFT) can be applied to convert the temperature derivative series intothe frequency domain, and thus generate a spectrum of time series oftemperature differences for each sensor location. The derivative of thespectrum, with respect to the frequency, can be generated. The amplitudeand phase of the frequency-derivative spectrum (e.g., the real andimaginary parts of the complex frequency-derivative spectrum) can thenbe determined. For example, using the heating cycle period, to, the realand imaginary values of the spectrum at the fundamental frequency of theN-pulse train can be selected at f₀=1/t₀.

The amplitude and phase of the frequency-derivative spectrum at eachsensor location thus corresponds to certain characteristics of themedium surrounding the sensing cable 101 at a particular sensorlocation. For example, the amplitude and phase can decreasemonotonically with frequency so that higher frequency corresponds withlower response to a change in temperature from the heating element.Accordingly, lower frequencies can obtain significant heating responseand higher signals. Additionally, the imaginary part of the complexspectrum can be nearly linear with the frequency while the real part canexhibit linear behavior beyond certain frequency values. Therefore, thederivative of the transfer function spectrum with respect to frequencycan correspond to the linear relationship of the temperature change withlog(t) in the time domain. In this manner, the amplitude and phase ofsensor locations exposed to deposit can be distinguishable from theamplitude and phase of sensor locations exposed to other media in thevessel, such as oil, gas, solid deposit (e.g., coking) or othereffluent.

The sensing cable 101 can be calibrated, e.g., with the control unit.Calibration can include, for example, calibrating the sensor array todetermine the amplitude and phase of the frequency-derivative spectrumof certain known media. For example, a number of materials with knownthermal properties can be measured for a broad range of values and adatabase can be constructed including correlations between the generatedamplitude and phase and characteristics of the known materials. Thedatabase can then be used as to determine characteristics surroundingmedium at a particular sensor location in the vessel, including themedium's composition, size, amount, and/or location.

The control unit 106, with reference to the known locations of eachsensor and the corresponding amplitude and phase of thefrequency-derivative spectrum, can detect the location and/or othercharacteristics (such as size) of different deposits in the vessel 810.To determine the location of a deposit, e.g., deposit 825 on wash bed820, the control unit can be configured to store the known position ofeach sensor location in one or more memories. For example, for a 36 inchlong sensing cable, having 36 sensor locations each spaced apart by aunit inch, positioned about the surface of a 36 inch wash bed 820, thecontrol unit can store the distance of each sensor location from thewall of the vessel 810 (i.e., for sensor location i={1, 2, . . . , 36},the control unit can store a corresponding distance measurement D_(i)={1in, 2 in, . . . , 36 in}). For each sensor location, i, the control unitcan determine the amplitude and phase of the frequency derivativespectrum as disclosed herein. With reference to, for example, a databasestoring the amplitude and phase of the frequency derivative spectrum forknown deposits, the control unit can thus determine whether each sensorlocation is in proximity to a deposit using the determined amplitude andphase at each sensor location.

Additionally or alternatively, and as embodied herein, the control unitcan process the determined amplitude or phase of the frequencyderivative spectrum of adjacent sensor locations to detect deposits.That is, for example, assuming the vessel contains media with otherwiseconstant characteristics, a change in the amplitude across two sensorlocations can correspond to deposit between those sensors. Likewise, achange in the phase can correspond to a deposit. In certain embodiments,the control unit can process both the amplitude and phase of adjacentsensors to enhance detection of deposits. For example, a change in boththe amplitude and phase can correspond to a deposit. Moreover, incertain embodiments, the control unit can monitor the amplitude andphase of each sensor location over time (e.g., throughout the operationof a VPS distillation tower 810) and determine whether the temperatureprofile of one or more sensor locations changes with time. For example,the control unit can be configured to monitor the temperature profile ofone or more sensor locations over time, identify a change in saidtemperature profile and, with reference, e.g., to a database of knowncharacteristics corresponding to a deposit, detect the formation of adeposit.

For purpose of illustration, and not limitation, description will now bemade of an exemplary method for detecting coking in a wash bed of a VPSdistillation tower. Passive temperature measurements can be taken ateach sensor location along the sensing cable to detect vapor/liquiddistribution. Because hydrocarbon vapor within the VPS distillationtower generally will be warmer than wash oil (e.g., Vacuum Gas Oil[“VGO”]), sensor locations surrounded by the wash oil can be identifiedas having a lower absolute temperature during passive temperaturemeasurement. A defined waveform of electrical pulse (e.g., a squarewave) can be propagated along the length of the sensing cable via, e.g.,a heating wire. The temperature profile at each sensor location can bemonitored using the fiber optic sensor array and optical signalinterrogator. As described above, the temperature change at each sensorlocation along the sensing cable corresponds to the thermalcharacteristics of the media surrounding the sensor location. Thus,variations of the temperature profiles along at sensor locations alongthe sensing cable can be used directly to indicate the location andamount of coking. Additionally, the log-time regression and frequencyspectrum methods disclosed herein can be used to further enhancedetermination of the thermal characteristics of the media surroundingthe sensor locations, and thus the degree and location of a deposit.Because wet resid deposit and VGO wash oil can have different thermalcharacteristics, wet resid deposition on the sensing cable can bedetected before the resid starts to coke. The heating element can thenbe turned off, and the corresponding decrease in temperature untilthermal equilibrium is reached, at each sensor location can be measuredto detect and confirm coking and non-coking regions along the sensingcable in dry and wet regions separately. Detecting the coking formationat an early stage and knowing its location within the wash bed in a VPSdistillation tower can allow for mitigation strategies, such as a highflow rate of wash oil to remove the coking.

In another exemplary embodiment, for purpose of illustration, multiplelayers of sensors can be deployed between different layers of packingmaterials, for example as depicted in FIG. 8. Measurement from eachlayer of sensor can reveal localized conditions, such as whether eachsensor location is in proximity to coking, VGO wash oil, vapor, or thelike. Measurement from each layer of sensors can reveal their localizedconditions (dry, et, coking or liquid flow rate), and entrainment ofresid can be inferred by comparison of those measurement results acrosssensor layers.

The techniques disclosed herein can provide for continuous depositsensing, such as coking or fouling, in real time. No moving mechanicalparts need be included inside the sensing cable. Because materialthermal properties can be measured for deposit detection, themeasurement results can be independent of electrical conductivity,salinity, and crude oil constituents, such as sulfur, ironsulfide/oxide. Moreover, relative temperature changes before and afterheating/cooling can be used to infer material thermal properties fordeposit detection, and temperature baseline can be taken each timebefore heating/cooling is applied. Accordingly, the techniques disclosedherein need not require long term stability for temperature sensors.

Moreover, the system disclosed herein can operate at temperaturesranging from cryogenic temperatures up to over 1000° C. The size of thesensing cable can be relatively small (e.g., compared to conventionalthermocouples) and can be cost effective for large area coverage with alarge amount of sensors. Utilizing cost-effective optical fibertemperature sensors, the system disclosed herein can incorporate a largenumber of sensors, and can offer a high spatial resolution, e.g., lessthan 1 mm, over a long measurement range, e.g., several meters tokilometers. The diameter of the compact sensing cable can small, e.g.,less than 2 mm. The small diameter of the sensing cable can allow formeasurement in a tight space with reduced intrusiveness. Furthermore,the heating/cooling element can be turned off, and the sensing cable canbe converted to a temperature sensor, which can provide absolutetemperature measurements inside the vessel, such as measurements of thewash bed packing materials. Such absolute temperature measurements canbe used to infer liquid/vapor distributions, for example, inside packingmaterials.

Additional Embodiments

Additionally or alternately, the invention can include one or more ofthe following embodiments.

Embodiment 1

A method for detecting a deposit in a vessel, comprising: providingwithin a vessel a sensing cable including an optical fiber sensor arrayaligned with a heating element; propagating at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable;measuring, over time, a temperature profile of the sensing cablecorresponding to the heat pulse at each of a plurality of sensorlocations on the optical fiber sensor array; and detecting a deposit bydetermining one or more properties of the one or more media exposed tothe sensing cable at each of the plurality of sensor locations based onthe temperature profile corresponding thereto.

Embodiment 2

the method of any one of the previous embodiments, wherein the vesselincludes a vacuum pipe still distillation tower, a reactor, a heatexchanger, or a furnace tube.

Embodiment 3

the method of any one of the previous embodiments, wherein detecting thedeposit includes detecting one or more of debris, bio-growth, inorganicfouling, organic fouling, and coking.

Embodiment 4

the method of any one of the previous embodiments, wherein measuring,over time, the temperature profile includes measuring using fiber Bragggrating array based sensing, Raman scattering based sensing, Rayleighscattering based sensing, or Brillioun scattering based sensing.

Embodiment 5

the method of any one of the previous embodiments, wherein the heatingelement includes a resistive heating element and wherein propagating theat least one heat pulse includes applying an electrical pulse with apredetermined frequency and predetermined waveform.

Embodiment 6

the method of any one of the previous embodiments, wherein propagatingat least one heat pulse through the heating element includes propagatingthe at least one heat pulse through a heating element aligned adjacentto the optical fiber sensor array.

Embodiment 7

the method of embodiments 1, 2, 3, 4 or 5, wherein propagating at leastone heat pulse through the heating element includes propagating the atleast one heat pulse through a heating element disposed concentricallywith the optical fiber sensor array.

Embodiment 8

the method embodiments 1, 2, 3, 4, 6 or 7, wherein the heating elementincludes a thermoelectric device and wherein propagating at least oneheat pulse through the heating element includes propagating coolingpulse.

Embodiment 9

the method of any one of the previous embodiments, further comprisingcoating the sensing cable with a coating having a fouling affinityrepresentative of the vessel.

Embodiment 10

the method of any one of the previous embodiments, wherein the sensingcable further includes an outer diameter including a metal and mineralinsulation material.

Embodiment 11

the method of any one of the previous embodiments, wherein measuring thetemperature profile corresponding to the heat pulse at each of theplurality of sensor locations includes, for each sensor location,measuring at least a heating temperature measurement during propagationof the heat pulse over the sensor location, a peak temperaturemeasurement, and a cooling temperature measurement after propagation ofthe heat pulse over the sensor.

Embodiment 12

the method of embodiment 11, wherein detecting the deposit includescalculating a difference in the heating temperature measurement, thepeak temperature measurement, the cooling temperature measurement, orcombination thereof, between sensor locations, wherein the differenceindicates a deposit proximal at least one of the plurality of sensorlocations if the difference exceeds a predetermined threshold.

Embodiment 13

the method of any one of the previous embodiments, wherein measuring thetemperature profile corresponding to the heat pulse at each of theplurality of sensor locations includes, for each sensor location,measuring a plurality of temperatures over a period of time upon arrivalof the heat pulse at the sensor location.

Embodiment 14

the method of embodiment 13, wherein detecting the deposit includes, foreach temperature profile, performing a regression of the plurality oftemperatures over a logarithm of corresponding measurement times for apredetermined time window in the period of time to generate a slope andan intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.

Embodiment 15

the method of embodiment 14, wherein the predetermined time windowincludes a time window during a heating stage, the heating stagecorresponding to a period of time during propagation of the heat pulseover the sensor location or a time window during a cooling stage, thecooling stage corresponding to a period of time after propagation of theheat pulse over the sensor.

Embodiment 16

the method of embodiment 13, 14 or 15, wherein detecting the depositincludes, for each temperature profile: generating a time derivative bycalculating a derivative of the plurality of temperature measurementswith respect to time; applying a transform to the time derivative togenerate a complex spectrum; and determining an amplitude and a phase ofthe complex spectrum, wherein the amplitude and the phase of the complexspectrum relate to the one or more properties of the material exposed tothe sensing cable at the sensor location.

Embodiment 17

the method of embodiment 16, wherein detecting the deposit furtherincludes, for each temperature profile: generating a frequencyderivative spectrum by calculating the derivative of the complexspectrum with respect to frequency; and determining an amplitude and aphase of the frequency derivative spectrum, wherein the amplitude andthe phase of the frequency derivative spectrum relate to the one or moreproperties of the material exposed to the sensing cable at the sensorlocation.

Embodiment 18

the method of any one of the previous embodiments, wherein detecting thedeposit further includes monitoring the temperature profilecorresponding to each of the plurality of sensor locations, andcomparing the monitored temperature profiles to predeterminedtemperature profiles corresponding to deposit growth.

Embodiment 19

the method of any one of the previous embodiments, wherein detecting thedeposit further includes monitoring a first temperature profilecorresponding to each of the plurality of sensor locations and at leasta second temperature profile corresponding to each of the plurality ofsensor locations, and comparing the first and second temperatureprofiles to detect a change corresponding to deposit growth.

Embodiment 20

the method of any one of the previous embodiments, wherein the vesselhas an operating temperature between cryogenic temperatures andapproximately 1000° C., wherein the sensing cable has a diameter of lessthan 2 mm, and wherein the optical signal interrogator is configured tomeasure the temperature profile at a spatial resolution less than 1 mm.

Embodiment 21

A system for detecting a deposit in a vessel, comprising: a sensingcable including an optical fiber sensor array aligned with a heatingelement disposed in the vessel, the optical fiber sensor array having aplurality of sensor locations; an excitation source coupled with theheating element and configured to propagate at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable; anoptical signal interrogator coupled with the optical fiber sensor arrayand adapted to receive a signal from each of the plurality of sensorlocations and configured to measure, over time, a temperature profile ofthe sensing cable corresponding to the heat pulse at each of theplurality of sensor locations on the optical fiber sensor array; and acontrol unit, coupled with the heating element and the optical signalinterrogator, to detect a deposit by determining one or more propertiesof the one or more media exposed to the sensing cable at each of theplurality of sensor locations based on the temperature profilecorresponding thereto.

Embodiment 22

the system of embodiment 21, wherein the vessel includes a vacuum pipestill distillation tower, a reactor, a heat exchanger, or a furnacetube.

Embodiment 23

the system of embodiments 21 or 22, wherein the deposit includes one ormore of debris, bio-growth, inorganic fouling, organic fouling, andcoking.

Embodiment 24

the system of embodiments 21, 22 or 23, wherein the optical fiber sensorarray and the optical signal interrogator include a fiber Bragg gratingarray based sensing system, a Raman scattering based sensing system, aRayleigh scattering based sensing system, or a Brillioun scatteringbased sensing system.

Embodiment 25

the system of embodiments 21, 22, 23 or 24, wherein the heating elementincludes a resistive heating element and wherein the excitation sourceis configured to propagate an electrical pulse with a predeterminedfrequency and predetermined waveform, the electrical pulse correspondingto the at least one heat pulse.

Embodiment 26

the system of embodiments 21, 22, 23, 24 or 25, wherein the heatingelement is aligned adjacent to the optical fiber sensor array.

Embodiment 27

the system of embodiments 21, 22, 23, 24 or 25, wherein the heatingelement is disposed concentrically with the optical fiber sensor array.

Embodiment 28

the system of embodiments 21, 22, 23, 24, 26 or 27, wherein the heatingelement includes a thermoelectric device and wherein the at least oneheat pulse including a cooling pulse.

Embodiment 29

the system of embodiments 21, 22, 23, 24, 25, 26, 27 or 28 wherein thesensing cable further includes a coating having a fouling affinityrepresentative of the vessel.

Embodiment 30

the system of embodiments 21, 22, 23, 24, 25, 26, 27, 28 or 29, whereinthe sensing cable further includes an outer diameter including a metaland mineral insulation material.

Embodiment 31

the system of embodiments 21, 22, 23, 24, 25, 26, 27, 28, 29 or 30,wherein the optical signal interrogator is configured, for each of theplurality of sensor locations, to measure at least a heating temperaturemeasurement during propagation of the heat pulse over the sensorlocation, a peak temperature measurement, and a cooling temperaturemeasurement after propagation of the heat pulse over the sensor.

Embodiment 32

the system of embodiment 31, wherein the control unit is configured tocalculate a difference in the heating temperature measurement, the peaktemperature measurement, the cooling temperature measurement, orcombination thereof between adjacent sensor locations, wherein thedifference indicates a deposit proximal at least one of the plurality ofsensor locations if the difference exceeds a predetermined threshold.

Embodiment 33

the system of embodiments 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 or32, wherein the optical signal interrogator is configured, for each ofthe plurality of sensor locations, to measure a plurality oftemperatures over a period of time upon arrival of the heat pulse at thesensor location.

Embodiment 34

the system of embodiments 33, wherein the control unit is configured,for each temperature profile, to perform a regression of the pluralityof temperatures over a logarithm of corresponding measurement times fora predetermined time window in the period of time to generate a slopeand an intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.

Embodiment 35

the system of embodiments 34, wherein the predetermined time windowincludes a time window during a heating stage, the heating stagecorresponding to a period of time during propagation of the heat pulseover the sensor location or a time window during a cooling stage, thecooling stage corresponding to a period of time after propagation of theheat pulse over the sensor.

Embodiment 36

the system of embodiments 33, 34 or 35, wherein the control unit isconfigured, for each temperature profile, to: generate a time derivativeby calculating a derivative of the plurality of temperature measurementswith respect to time; apply a transform to the time derivative togenerate a complex spectrum; and determine an amplitude and a phase ofthe complex spectrum, wherein the amplitude and the phase of the complexspectrum relate to the one or more properties of the material exposed tothe sensing cable at the sensor location.

Embodiment 37

the system of embodiments 36, wherein the control unit is furtherconfigured, for each temperature profile, to: generate a frequencyderivative spectrum by calculating the derivative of the complexspectrum with respect to frequency; and determine an amplitude and aphase of the frequency derivative spectrum, wherein the amplitude andthe phase of the frequency derivative spectrum relate to the one or moreproperties of the material exposed to the sensing cable at the sensorlocation.

Embodiment 38

the system of embodiments 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,32, 33, 34, 35, 36 or 37, wherein the control unit is further configuredto monitor the temperature profile corresponding to each of theplurality of sensor locations, and compare the monitored temperatureprofiles to predetermined temperature profiles corresponding to depositgrowth.

Embodiment 39

the system of embodiments 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,32, 33, 34, 35, 36, 37 or 38, wherein the control unit is furtherconfigured to monitor a first temperature profile corresponding to eachof the plurality of sensor locations and at least a second temperatureprofile corresponding to each of the plurality of sensor locations, andcomparing the first and second temperature profiles to detect a changecorresponding to deposit growth.

Embodiment 40

the system of embodiments 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,32, 33, 34, 35, 36, 37, 38 or 39, wherein the vessel has an operatingtemperature between cryogenic temperatures and approximately 1000° C.,wherein the sensing cable has a diameter of less than 2 mm, and whereinthe optical signal interrogator is configured to measure the temperatureprofile at a spatial resolution less than 1 mm.

While the disclosed subject matter is described herein in terms ofcertain exemplary embodiments, those skilled in the art will recognizethat various modifications and improvements can be made to the disclosedsubject matter without departing from the scope thereof. Moreover,although individual features of one embodiment of the disclosed subjectmatter can be discussed herein or shown in the drawings of the oneembodiment and not in other embodiments, it should be apparent thatindividual features of one embodiment can be combined with one or morefeatures of another embodiment or features from a plurality ofembodiments.

In addition to the specific embodiments claimed below, the disclosedsubject matter is also directed to other embodiments having any otherpossible combination of the dependent features claimed below and thosedisclosed above. As such, the particular features presented in thedependent claims and disclosed above can be combined with each other inother manners within the scope of the disclosed subject matter such thatthe disclosed subject matter should be recognized as also specificallydirected to other embodiments having any other possible combinations.Thus, the foregoing description of specific embodiments of the disclosedsubject matter has been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit thedisclosed subject matter to those embodiments disclosed.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the method and system of thedisclosed subject matter without departing from the spirit or scope ofthe disclosed subject matter. Thus, it is intended that the disclosedsubject matter include modifications and variations that are within thescope of the appended claims and their equivalents.

What is claimed is:
 1. A method for detecting a deposit in a vessel,comprising: providing within a vessel a sensing cable including anoptical fiber sensor array aligned with a heating element; propagatingat least one heat pulse through the heating element along at least aportion of the sensing cable to affect an exchange of thermal energybetween the heating element and the one or more media exposed to thesensing cable; measuring, over time, a temperature profile of thesensing cable corresponding to the heat pulse at each of a plurality ofsensor locations on the optical fiber sensor array; and detecting adeposit by determining one or more properties of the one or more mediaexposed to the sensing cable at each of the plurality of sensorlocations based on the temperature profile corresponding thereto.
 2. Themethod of claim 1, wherein the vessel includes a vacuum pipe stilldistillation tower, a reactor, a heat exchanger, or a furnace tube. 3.The method of claim 1, wherein detecting the deposit includes detectingone or more of debris, bio-growth, inorganic fouling, organic fouling,and coking.
 4. The method of claim 1, wherein measuring, over time, thetemperature profile includes measuring using fiber Bragg grating arraybased sensing, Raman scattering based sensing, Rayleigh scattering basedsensing, or Brillioun scattering based sensing.
 5. The method of claim1, wherein the heating element includes a resistive heating element andwherein propagating the at least one heat pulse includes applying anelectrical pulse with a predetermined frequency and predeterminedwaveform.
 6. The method of claim 1, wherein propagating at least oneheat pulse through the heating element includes propagating the at leastone heat pulse through a heating element aligned adjacent to the opticalfiber sensor array.
 7. The method of claim 1, wherein propagating atleast one heat pulse through the heating element includes propagatingthe at least one heat pulse through a heating element disposedconcentrically with the optical fiber sensor array.
 8. The method ofclaim 1, wherein the heating element includes a thermoelectric deviceand wherein propagating at least one heat pulse through the heatingelement includes propagating cooling pulse.
 9. The method of claim 1,further comprising coating the sensing cable with a coating having afouling affinity representative of the vessel.
 10. The method of claim1, wherein the sensing cable further includes an outer diameterincluding a metal and mineral insulation material.
 11. The method ofclaim 1, wherein measuring the temperature profile corresponding to theheat pulse at each of the plurality of sensor locations includes, foreach sensor location, measuring at least a heating temperaturemeasurement during propagation of the heat pulse over the sensorlocation, a peak temperature measurement, and a cooling temperaturemeasurement after propagation of the heat pulse over the sensor.
 12. Themethod of claim 11, wherein detecting the deposit includes calculating adifference in the heating temperature measurement, the peak temperaturemeasurement, the cooling temperature measurement, or combinationthereof, between sensor locations, wherein the difference indicates adeposit proximal at least one of the plurality of sensor locations ifthe difference exceeds a predetermined threshold.
 13. The method ofclaim 1, wherein measuring the temperature profile corresponding to theheat pulse at each of the plurality of sensor locations includes, foreach sensor location, measuring a plurality of temperatures over aperiod of time upon arrival of the heat pulse at the sensor location.14. The method of claim 13, wherein detecting the deposit includes, foreach temperature profile, performing a regression of the plurality oftemperatures over a logarithm of corresponding measurement times for apredetermined time window in the period of time to generate a slope andan intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.
 15. The method of claim 14,wherein the predetermined time window includes a time window during aheating stage, the heating stage corresponding to a period of timeduring propagation of the heat pulse over the sensor location or a timewindow during a cooling stage, the cooling stage corresponding to aperiod of time after propagation of the heat pulse over the sensor. 16.The method of claim 13, wherein detecting the deposit includes, for eachtemperature profile: generating a time derivative by calculating aderivative of the plurality of temperature measurements with respect totime; applying a transform to the time derivative to generate a complexspectrum; and determining an amplitude and a phase of the complexspectrum, wherein the amplitude and the phase of the complex spectrumrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.
 17. The method of claim 16,wherein detecting the deposit further includes, for each temperatureprofile: generating a frequency derivative spectrum by calculating thederivative of the complex spectrum with respect to frequency; anddetermining an amplitude and a phase of the frequency derivativespectrum, wherein the amplitude and the phase of the frequencyderivative spectrum relate to the one or more properties of the materialexposed to the sensing cable at the sensor location.
 18. The method ofclaim 1, wherein detecting the deposit further includes monitoring thetemperature profile corresponding to each of the plurality of sensorlocations, and comparing the monitored temperature profiles topredetermined temperature profiles corresponding to deposit growth. 19.The method of claim 1, wherein detecting the deposit further includesmonitoring a first temperature profile corresponding to each of theplurality of sensor locations and at least a second temperature profilecorresponding to each of the plurality of sensor locations, andcomparing the first and second temperature profiles to detect a changecorresponding to deposit growth.
 20. The method of claim 1, wherein thevessel has an operating temperature between cryogenic temperatures andapproximately 1000° C., wherein the sensing cable has a diameter of lessthan 2 mm, and wherein the optical signal interrogator is configured tomeasure the temperature profile at a spatial resolution less than 1 mm.21. A system for detecting a deposit in a vessel, comprising: a sensingcable including an optical fiber sensor array aligned with a heatingelement disposed in the vessel, the optical fiber sensor array having aplurality of sensor locations; an excitation source coupled with theheating element and configured to propagate at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable; anoptical signal interrogator coupled with the optical fiber sensor arrayand adapted to receive a signal from each of the plurality of sensorlocations and configured to measure, over time, a temperature profile ofthe sensing cable corresponding to the heat pulse at each of theplurality of sensor locations on the optical fiber sensor array; and acontrol unit, coupled with the heating element and the optical signalinterrogator, to detect a deposit by determining one or more propertiesof the one or more media exposed to the sensing cable at each of theplurality of sensor locations based on the temperature profilecorresponding thereto.
 22. The system of claim 21, wherein the vesselincludes a vacuum pipe still distillation tower, a reactor, a heatexchanger, or a furnace tube.
 23. The system of claim 21, wherein thedeposit includes one or more of debris, bio-growth, inorganic fouling,organic fouling, and coking.
 24. The system of claim 21, wherein theoptical fiber sensor array and the optical signal interrogator include afiber Bragg grating array based sensing system, a Raman scattering basedsensing system, a Rayleigh scattering based sensing system, or aBrillioun scattering based sensing system.
 25. The system of claim 21,wherein the heating element includes a resistive heating element andwherein the excitation source is configured to propagate an electricalpulse with a predetermined frequency and predetermined waveform, theelectrical pulse corresponding to the at least one heat pulse.
 26. Thesystem of claim 21, wherein the heating element is aligned adjacent tothe optical fiber sensor array.
 27. The system of claim 21, wherein theheating element is disposed concentrically with the optical fiber sensorarray.
 28. The system of claim 21, wherein the heating element includesa thermoelectric device and wherein the at least one heat pulseincluding a cooling pulse.
 29. The system of claim 21, wherein thesensing cable further includes a coating having a fouling affinityrepresentative of the vessel.
 30. The system of claim 21, wherein thesensing cable further includes an outer diameter including a metal andmineral insulation material.
 31. The system of claim 21, wherein theoptical signal interrogator is configured, for each of the plurality ofsensor locations, to measure at least a heating temperature measurementduring propagation of the heat pulse over the sensor location, a peaktemperature measurement, and a cooling temperature measurement afterpropagation of the heat pulse over the sensor.
 32. The system of claim31, wherein the control unit is configured to calculate a difference inthe heating temperature measurement, the peak temperature measurement,the cooling temperature measurement, or combination thereof betweenadjacent sensor locations, wherein the difference indicates a depositproximal at least one of the plurality of sensor locations if thedifference exceeds a predetermined threshold.
 33. The system of claim21, wherein the optical signal interrogator is configured, for each ofthe plurality of sensor locations, to measure a plurality oftemperatures over a period of time upon arrival of the heat pulse at thesensor location.
 34. The system of claim 33, wherein the control unit isconfigured, for each temperature profile, to perform a regression of theplurality of temperatures over a logarithm of corresponding measurementtimes for a predetermined time window in the period of time to generatea slope and an intercept of the regression, wherein the slope and theintercept relate to the one or more properties of the material exposedto the sensing cable at the sensor location.
 35. The system of claim 34,wherein the predetermined time window includes a time window during aheating stage, the heating stage corresponding to a period of timeduring propagation of the heat pulse over the sensor location or a timewindow during a cooling stage, the cooling stage corresponding to aperiod of time after propagation of the heat pulse over the sensor. 36.The system of claim 33, wherein the control unit is configured, for eachtemperature profile, to: generate a time derivative by calculating aderivative of the plurality of temperature measurements with respect totime; apply a transform to the time derivative to generate a complexspectrum; and determine an amplitude and a phase of the complexspectrum, wherein the amplitude and the phase of the complex spectrumrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.
 37. The system of claim 36,wherein the control unit is further configured, for each temperatureprofile, to: generate a frequency derivative spectrum by calculating thederivative of the complex spectrum with respect to frequency; anddetermine an amplitude and a phase of the frequency derivative spectrum,wherein the amplitude and the phase of the frequency derivative spectrumrelate to the one or more properties of the material exposed to thesensing cable at the sensor location.
 38. The system of claim 21,wherein the control unit is further configured to monitor thetemperature profile corresponding to each of the plurality of sensorlocations, and compare the monitored temperature profiles topredetermined temperature profiles corresponding to deposit growth. 39.The system of claim 21, wherein the control unit is further configuredto monitor a first temperature profile corresponding to each of theplurality of sensor locations and at least a second temperature profilecorresponding to each of the plurality of sensor locations, andcomparing the first and second temperature profiles to detect a changecorresponding to deposit growth.
 40. The system of claim 21, wherein thevessel has an operating temperature between cryogenic temperatures andapproximately 1000° C., wherein the sensing cable has a diameter of lessthan 2 mm, and wherein the optical signal interrogator is configured tomeasure the temperature profile at a spatial resolution less than 1 mm.